Minimum-variance portfolio weight

MediumStatistics Finance & Derivatives~5m

Two uncorrelated assets have volatilities $\sigma_A=20\%$ and $\sigma_B=30\%$ . Across all long portfolios $w_A+w_B=1$ , what weight $w_A$ in asset $A$ minimizes the portfolio's variance? Give a decimal to four places.

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Write $\sigma_p^2(w_A)$ with $w_B=1-w_A$ , then differentiate and set to 0.
$w_A=\sigma_B^2/(\sigma_A^2+\sigma_B^2)=0.09/0.13$ .

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0.6923 (± 0.001)

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Minimum-variance portfolio weight

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